


To every crop there is a season, and a time for every moon: Astrophysics & climatology in the Quad

by Grimview, Hagar



Category: Killjoys (TV)
Genre: Arkyn, Astrophysics, Climatology, Fanart, Fanwork Research & Reference Guides, Gen, Leith - Freeform, Math-Free, Meta, Qresh, Qresh is an epic disaster, Season 01, The Quad, The creators are dorks, Westerly - Freeform
Language: English
Status: Completed
Published: 2015-10-09
Updated: 2015-10-09
Packaged: 2018-04-25 13:59:29
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 2
Words: 6,119
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/4963330
Author URL: https://archiveofourown.org/users/Grimview/pseuds/Grimview, https://archiveofourown.org/users/Hagar/pseuds/Hagar
Summary: <blockquote class="userstuff">
              <p>Why is Qreshi landmass submerged? How many seasons does Leith have? In this work, we combine canon information and basic astrophysics to make some (mostly) educated guesses on what the planetary system of the Quad behaves like, and what this means for the people who live there.</p>
            </blockquote>





	1. Chapter 1

**Author's Note:**

> This started as part of the [Fact Sheet](http://archiveofourown.org/works/4857245). Then we wrote the first draft, read it, and thought better of it.
> 
> This essay wouldn’t be anywhere near as readable and accessible as (we hope) it is without the help of [Pameluke](http://archiveofourown.org/users/Pameluke) and [misslucy21](http://archiveofourown.org/users/misslucy21). Ladies, your help was indispensable; thank you, and thank you again.
> 
> We would be absolutely delighted if anyone has any comments, questions or corrections.

### Preface

A significant portion of Qresh’s landmass is submerged under its ocean. Though this land is sometimes reclaimed, and routinely enough so that there exist rituals for that sort of a thing (s01e01 _Bangarang_ ), submersion has last happened as recent as two generations pre-canon (s01e03 _The Harvest_ ). This has been going on long enough for Qresh to terraform and colonize two of its moons, well over seven generations. Westerly had been mined and otherwise used enough to cause significant climate changes that make much of its surface unlivable for humans; meanwhile, Leith is a prospering agricultural center with the harvest season of one of its main crops (hokk) lasting a full half a year (s01e03).

 _Killjoys_ canon tells us all of this. Things it doesn’t tell us include the length of a year, the seasons on Leith, or the root cause of Qresh’s oceans and landmass submersion issues. The goal of this work is to try and understand what’s going on in the Quad with regards to climate, day-and-night cycles and other related matters. To this end, we interpret and infer from canon information using some basic astrophysics.

It bears noting that the purpose of this work is _not_ to decide what the Quad “must” be like, or to otherwise impose scientific order and authority. Rather, this is a fannish interpretation that makes sense and appeals to the authors at the time this work is posted. Fellow fans are absolutely welcome to draw on the ideas below, but we do not _expect_ anyone to do so.

 

### Size matters from a distance: Astrophysics for fandom

The first thing we must do is present the relevant astrophysical terms and concepts. We do not purport to provide an exhaustive explanation, nor will you find any mathematical formulas here (though concepts like “square root” are mentioned). Recommended external sources are referred to where relevant, but they shouldn’t be necessary to understand the speculative portions of this essay.

 _Gravity._ Gravity is a force: that is to say, it does things to other things. The magnitude of gravity (the forcefulness of the force) is determined by two things: the mass of the objects involved, and the distances between them. The effect of mass on gravity is direct: an object that has twice as much mass exerts twice as much force. The effect of distance on gravity is square and inverse: an object that is twice as far exerts four times less force. Things are simple enough when only two objects are involved, but get quite tricky otherwise. If any of the objects were in motion to start with, or if any other forces are involved, then things get even trickier. The gravitational force with which a planet pulls on things is denoted by the small letter _g_. (From here on, where we use the word “gravity” unqualified, we mean _g_.) _g_ is directly related to the planet’s mass and inversely related to the cube of the planet’s radius (distance from the center of its core to its surface), denoted with the small letter _r._

 _Mass vs. Weight._ The word “mass”, used in the above paragraph, means the amount of a thing. The word “weight” refers to the way this mass is held down by a planet’s (or a moon’s) gravitational pull. The two words may be used interchangeably on Earth, but not everywhere else. A person who weighs 60kg on Earth will only weigh 10kg on the moon, though they didn’t “lose any weight” : the moon’s _g_ is six times smaller than the Earth’s, so the same person with the same mass weighs six time less on the moon than on Earth. This makes living on the moon (as opposed to just visiting there) a real health hazard. Human bodies are adapted to the Earth’s gravity. Over the long term, gravity that’s too high or too low will harm the human body or otherwise cause irreversible physiological changes. For humans to prosper, we need the gravity to be within a fairly narrow range.

 _Density._ The same mass doesn’t always take up the same amount of space: a kilogram of iron (or water) makes a fairly small dumbbell, but a kilogram of confetti makes a fairly big bag. That’s because iron and water are both more _dense_ than confetti. Density is defined as the ratio between a certain mass, and the amount of space this mass takes up. The relationship between density and mass is direct and linear: more mass makes the same space more dense, and twice the mass makes the same space twice as dense. The relationship between the size of a space (its volume) and its density is inverse, not direct: the same mass in a space twice as big makes for one-eighth the density. This is because the volume of a spherical object, like a planet or a moon, is directly related to its _r_. However, this relationship is not linear. Rather, a sphere’s volume is the product of _r_ to the third power: an _r_ twice as big makes for eight times the volume, and an _r_ three times as big makes for 27 times the volume. As density is inversely related to volume, twice the _r_ makes an object eight times less dense and thrice the _r_ makes an object 27 times less dense.

 _Planetary density._ Some planets are made primarily of gas; others are made primarily of solids. Gaseous planets (like Neptune or Jupiter) have a really low density. The density of terrestrial planets (like Earth or Mars) is much higher. For a sense of scale, consider that Mars’s density (about 80% of Earth’s), while low, is about twice the maximum density of a gaseous planet. Denser terrestrial planets are smaller (next to other planets of the same mass) - and more likely to contain all sorts of interesting metals.

 _Planetary rotations 1: diurnal periods._ The reason Earth has day and night cycles is not because it orbits the sun. Rather, it’s because Earth rotates on its axis. You can visualize it by holding up an orange (or a similar object) in front of a lamp and turning it around. The time it takes a planet to complete a single rotation along its axis (that is, a single day-and-night cycle) is called a _diurnal period._

 _Do moons have diurnal periods?_ Well, that depends. A moon’s self-rotation (or lack thereof), whether it circles the planet around its equator (or at an angle to it, and if so at which angle) and whether the planet (or other moons circling it) get between a specific moon and the sun (and if so how often) - all of these play a part in determining whether a moon has a diurnal period or something resembling it. We’ll discuss in detail two options: tidal locking, and regular shading events.

 _Tidal lock._ If a moon is tidally locked then one side of it always faces the planet and the other always away from it. Tidal locking happens when a moon completes a single rotation on its axis in the same time it completes an orbit around its planet. For example, Earth’s moon is tidally locked; that’s why we can only ever see one side of it. However, the so-called “dark side of the moon” - the one facing away from Earth - still sees daylight. The moon has its own diurnal cycle, which is determined the same way as the Earth’s: by the moon’s self-rotation and axial tilt relative to the sun ( we’ll get to the moon’s tilt relative to the Earth in the section about tides). The moon’s diurnal period is visible to us: what part of the moon’s near side hangs lit and bright in our sky is in (moon-)daytime, and what part is dark (and so invisible, making the moon appear crescent-like) is in (moon-)nighttime. If you think that makes the moon’s diurnal period Earth’s month, you are absolutely correct.

 _Shading events._ “Shading” occurs when one astrophysical body (like a planet or a moon) is “in the shade” of another - that is, when the second body gets between the first and the sun and so causes the first body to experience a solar eclipse. Here on Earth, we experience two kinds of shading events: a solar eclipse when our moon gets between us and the sun and a lunar eclipse when the Earth gets between the moon and the sun. Should someone be observing from the moon, they’d experience an “Earth eclipse” in the former case (as the moon is blocking what light may illuminate the Earth and make it visible) and a solar eclipse in the latter (as the Earth is blocking what light may reach the surface of the moon). Eclipses of either kind are fairly infrequent for Earth and its moon. As a hypothetical alternative, consider that a moon which does not self-rotate (and so cannot have diurnal periods) may still have regular light and dark periods if shaded by its planet on a regular basis. What sorts of eclipses a celestial body experiences and at what frequency or regularly depends not only on the orbits of all objects involved (including their tilt) and their size - but also on their _apparent_ size.

 _Faraway objects may be a different size than they appear._ How big an object appears to us depends both on its size, and on its distance from us. For spherical objects like planets and moons, this relationship is mediated through a sine function. That’s not to say distance and actual size are the only factors that matter. It’s common-sense that the same object will appear a different size when viewed by the naked eye - or through a telescope. Likewise, a planet’s atmosphere (and its specific composition) also affects what we can see and how.

 _Planetary rotations 2: seasonal cycles._ A planet could rotate along its own axis and around its sun - and still have the same single season at all times. (Which season it would be depends on the planet’s distance from the sun, and the sun’s type: it could be anything from a Sahara summer to an Arctic winter - or, to wander outside the human-habitable zone, something like Martian cold or Venus’ violent, constant acid storms.) This is because at any point in its circle across the sun (that is, at any time in the year) the same spot on the planet will be hit by the same amount of solar radiation. To have multiple seasons, the planet must be tilted on its axis to some degree.The magnitude of seasonal variation across the planet is affected by several factors, including but not limited to the degree of tilt, the planet’s _r_ and the amount and dispersal of the planet’s water (oceans and lakes).

 

_Figure 1: Axial Tilt (Planetary). Top panel: self-rotation axis is perpendicular to the orbital plane. Bottom panel: axis is tilted relative to the orbital plane. In the top panel, the angle at which sunlight hits the continent (serving as a point of reference) is identical in both orbital positions. In the bottom panel, the angle is different between the right (northern hemisphere summer) and left (northern hemisphere winter) positions. In the top panel, the sun rises in the east and sets in the west everywhere on the planet. In the bottom panel, the sun rises in the southeast in the northern hemisphere and the northeast in the southern one, and sets in the southwest and the northwest, accordingly; only the equator observes sunrise and sunset at east and west, with the sun passing at the very middle of the sky (rather than south or north of it)._

 

 _Seasonal cycles 2: polar differences._ Seasons change not just with time, but also with physical location on the same planet. At any given point in time, different places on Earth experience different seasons. For example, the tropics (the area around the equator, the widest band of the globe) have no seasonal change caused by planetary motion. Outside the tropics, two places at the same distance from the equator but in different directions (one north and one south) will experience “opposite” seasons at any given time - if one is at the height of winter the other is at the height of summer, and vice-versa. The magnitude of seasonal variance between two places at two different distances from the equator (but in the same direction away from it) will also be different; for example, the summer-winter contrast in the arctic is more extreme than in New York. All these different climates (“climate” being the pattern of the seasons) are caused by Earth’s axial tilt: the tropics are always at the same angle to the sun, whereas everywhere else is not. The same factors  - the planet’s _r_ and the latitude of a specific location - also combine to affect diurnal variation: that is, the degree to which the number of daylight hours changes with the seasons. (Altitude - that is, vertical distance from the planet’s sea level - can affect climate in a way similar to increased distance from the equator; and large bodies of water such as oceans, seas and big lakes make the climate near them milder; but that’s getting rather too much climatology for this discussion.)

 _Seasonal cycles 3: a matter of size._ Distance from the equator can be measured either in absolute terms like kilometers or miles, or in relative ones like latitude, which is a measure of the relative distance between the equator and the poles: the whole of the globe is divided into 360 degrees, with the equator always marked 0 and the poles 180 degrees north or south of the equator. Suppose we have two planets, circling similar suns at the same distance and with identical axial tilts; however, one planet has triple the _r_ of the other one. (That is, it’s six times wider, has a surface nine times as big, and takes up 27 times as much space.) To reach the same latitude on each planet, one needs to travel an absolute distance nine times farther on the big planet as one would need to on  the small one. Absolute and relative distance from the equator both matter: the bigger a planet is, the more extreme the seasonal variation may be.  

 _The mystery of tides._ Tides are a prime example of the complex interactions caused by gravity. The solid parts of the Earth are not particularly affected by the moon’s gravitational force, but the oceans are more sensitive. Ocean water is pulled by the moon as it rotates around the Earth, causing the tide to rise on the moon-facing side of Earth and ebb on the other side of it. The rise and ebb of the tide are the most pronounced when the sun and the moon are on the same axis (spring tide) and least pronounced when they are at a straight angle to each other (neap tide). A tidal cycle is the period it takes the tide to complete one full rise and ebb. The orbit of most moons is in the same plane as their planet’s orbit around the sun, like two intersecting circles draw on paper. However, sometimes a moon orbit is tilted next to the planet’s (see Figure 2 below).

 

_Figure 2. Panel A: lunar orbit around planet in same plane as planetary orbit around sun. Panel B: lunar orbit around planet that is tilted relative to the plane of planetary orbit around sun._

 

The latter is the case with Earth’s moon.  As a result, Earth’s poles see only one high tide and one low tide within a day (diurnal tides) whereas the equator sees two high and two low tides per day (semi-diurnal tides). (Due to the Earth’s own tilt relative to the sun, equatorial regions have diurnal tides around the winter and summer solstices.) Those parts of Earth that are in the middle are, well, in the middle. And lastly, the timing of the tide shifts a little each day because the moon also rotates along its own axis, further altering the gravitational forces.

###### Suggested Resources

These are all resources we accessed in the process of preparing the above. They’re both reliable and readable (well, with the exception of the Wikipedia article; that one’s not designed for friendliness), and they go into the above concepts in a bit more depth than covered here - or else they’re just cool to play with.

  * [Angular diameter](https://en.wikipedia.org/wiki/Angular_diameter)
  * [Interactive model of our solar system](http://solarsystem.appzend.net/)
  * [What causes seasons?](http://www.timeanddate.com/astronomy/seasons-causes.html)
  * [Climate how and why](http://www.blueplanetbiomes.org/climate.htm)
  * [Earth’s tides, explained](http://oceanlink.island.net/oinfo/tides/tides.html)



 


	2. Chapter 2

### What’s in a Quad?

 _The Quad._ Killjoys canon tells us quite a bit about the Quad system. We know it has four terrestrial bodies of appropriate mass and density to support human life. Those bodies are Qresh, Leith, Westerly and Arkyn. Of these, Qresh is the biggest by far; the other three are referred to as its moons. (Syfy’s blog refers to Qresh as a “dwarf planet”, but that makes little sense: a “dwarf planet” would be an object at no bigger than about Pluto’s size, nowhere near big enough to either support human life or hold three human-life-sustaining moons. For a sense of scale, consider that a person weighing 60kg on Earth would only weigh 0.5kg on Pluto.) As seen from space any number of times in the show, Qresh appears rather Earth-like, primarily blue and green with some yellow and white; Leith appears primarily green, with little yellow or brown; Westerly is primarily red with some white; and Arkyn is grey, with a blue-green ring.

 _What it looks like._ Though there’s any number of shots showing each planet from space, there is only a handful of shots that give us any clue as to how they are located relative to each other. Episode s01e01 features a shot of the Quad as seen from an unknown vantage point in space; episodes s01e01 and s01e04 show the view of the sky from Qresh (once from an unknown location and once from Land Kendry); and s01e10 _Escape Velocity_ shows the sky from Arkyn. Though much of the show takes place on either Westerly or Leith, we do not get a shot of their sky. In the introductory shot, Leith and Westerly appear on one side of Qresh with Arkyn on the other; no other planets are visible at any point. The perspective makes it difficult to tell anything specific of the relative sizes of Qresh and the moons. From Qresh, Arkyn appears 5-9 times smaller than Westerly, once to its right and once to its left. From Arkyn, Leith appears behind Westerly to the left and Qresh to the right (apparent “east”, given the direction of light); Qresh appears about 5 times bigger than Westerly, and 11 times bigger than Leith.

 

_Figure 3: Shots indicating relative size and placement of terrestrial objects in the Quad. Top, left to right:  s01e01, view from space; s01e01, view from Qresh; s01e04, view from Qresh. Bottom: s01e01, view from Arkyn._

 

 _Climate and geography._ Qresh and Leith must have diurnal periods: Qresh because it was deemed fit for colonization and Leith - for agriculture. Westerly seems to have regular light-and-dark periods, but isn’t required to have them; and nothing is known of Arkyn. As Qresh and its moons are all by definition at the same effective distance from the local sun, any climate differences between them need be the product of other factors (such as tilt and geography). What we see of Qresh and Leith seems compatible with temperate climate or seasonal (some people wear multiple long layers, some show bare skin); Leith specifically is likely to have more than one season, as migrant Westerlyn workers employed in hokk agriculture spend only half the year there; Westerlyn Badlands seem quite hot; and Arkyn has visible ice on the surface, so it must be significantly below the freezing point. Qresh is explicitly said to have large bodies of water; these are also visible from space (blue). Leith must have enough water to support the agriculture (and visible greenery), but these water sources are not visible from orbit. Westerly and Arkyn both seem to be quite dry.

 _Qreshi land crisis._ Most of Qresh’s landmass is submerged (s01e01). This has been a problem with regards to Qresh’s population for well over seven generations (150-200yr; timeline), despite land being reclaimed often enough that formal reclamation ceremonies exist (s01e01). However, that is not enough to mitigate the land crisis, possibly because the submersion is not the product of a single long-ago catastrophe but rather an ongoing process: submersion is known to have occurred as recently as a generation and a half (30-50yr) pre-canon (s01e04).

 _Qreshi expansion._ The Company’s first attempt at terraforming Qresh’s moons was Arkyn (s01e10); second was Westerly, and Leith only last. This suggests that the initial drive for Qreshi expansion was not overpopulation due to the land crisis, but rather a shortage of natural resources. Recall Qresh was itself colonized; early in Qreshi settlement, it likely had a relatively small population and a high need for industry and construction. This, as well as a terraforming learning curve, may explain how and why Leith turned out that much more hospitable and pleasant to humans than Westerly. It’s also interesting to note that while Leithians all are impoverished Qreshi land-owners or their descendants, Westerlyns do not seem to come from the same background.

 _Context, context._ Above, we noted which terrestrial object in the Quad is visible from which, and at what apparent size. However, recall that apparent size depends on the distance between objects as much as it does on the observed object’s size. Additionally, planets and moons are constantly in motion and the distances between them may well (and likely do) change periodically. As a matter of fact, the most limiting canon information regarding the size of Qresh and its moons is that they are all of the appropriate mass-to-radius size to support reasonably-comfortable human existence - and that’s one hell of a requirement.

 _Mass, gravity, radius._ Gravity and density are both directly related to mass (the bigger the mass, the bigger both _g_ and density) and inversely related to _r_ (the bigger _r_ is, the smaller both _g_ and density). Both gravity and density are linearly related to mass: twice the mass means twice the gravity and, all else being equal, twice the density. However, the way _r_ affects gravity and density is not linear: half the radius means a four times increase in gravity and an eightfold increase in density, but a third of the radius would be nine times the gravity and 27 times the density.

 _Goldilocks’ planet._ Solid, terrestrial planets don’t come at all sizes. If their _r_ gets too big they either become a gas planet (if their density was low) or collapse in on themselves (if their density was high). Leith, Westerly and Arkyn are each of enough mass and density for human-comfortable _g_ \- and Qresh needs to be big enough to anchor all of them while still being dense enough to be solid, not so wide as to collapse, and of low enough mass to not crush human bones. For scale, consider that a planet of twice Earth’s _r_ and four times Earth’s mass will have the same _g_ as Earth, but only half the density - which means it’d be only barely solid. Qresh’s properties likely resemble this profile: four times as wide and heavy, about same gravity, but not held together particularly well. This low density (0.5-0.6 times that of Earth’s; Mars’ density is about 0.7 of Earth’s) correlates with Qresh’s known lack of natural resources of the kind made available through mining.

 _What are little moons made of?_ Arkyn and Westerly are known to be more lucrative for mining than Leith is. This suggests that their density is quite high. As Arkyn is presumed to have the smallest _r_ in the Quad, this would make it the densest as well as (potentially) of the highest gravity: if any terrestrial body in the Quad has uncomfortably high gravity, Arkyn is it.

 _QUADrupled._ In order for the Quad to hold together, Qresh and its moons all need to have just the right masses at just the right distances from each other while traveling at just the right speeds relative to each other. Canon information is limited: the apparent size of objects depends on entirely too many variables, including also atmospheric effects. All we know of Qresh’s atmosphere is that it’s breathable to humans; otherwise, we have no idea how it may affect visible light that passes through it. This is not enough to infer from - particularly considering how advanced the relevant math is. Luckily, science is also a fandom and scientists - like fans everywhere - love to share the squee. In the case of the astrophysics fandom, this means online simulators. We combined the mass/ _r_ ratio constants with a thorough exploration of the simulations to figure out what combination of masses, _r_ values and orbits could be stable. The results were one set of sizes (mass and _r,_ the combination of which determines density and _g_ ) and two possible sets of orbits.

 _Sizes._ As mentioned in the _Goldilocks’ planet_ paragraph above, Qresh is approximately twice as wide as Earth and 4 heavier to satisfy both density and gravity requirements. Based on the simulation, it seems like likely dimensions of Qresh are twice times Earth’s width and 4.5 times its mass, yielding half the density and a _g_ 12% higher (that is, a person weighing 50kg on Earth would weigh 56kg on Qresh). The likely dimensions for the three moons are as follows:

  * Leith: just under 1/3 Qresh’s width and 8% its mass, yielding 2.5 times the density and 80% of its _g_
  * Westerly: almost 40% of Qresh’s width and 14 times its mass, yieding 2.6 times the density and an effectively identical _g_
  * Arkyn: a sixth of of Qresh’s width and just under 3% its mass, yielding 6 times the density and an effectively identical _g_



 

 

_Figure 4: Size chart of Qresh and her daughters. Shown left to right are Qresh, Leith, Westerly and Arkyn._

 

 _Orbits._ The simulation yielded two sets of potentially stable orbits, depicted in Figure 5 below. These two configurations are rather different, but have a few common properties. First, each moon takes a different time to complete one orbit. Second, each moon’s speed changes throughout its orbit; this is because the gravitational forces between the bodies in the Quad change with the distances between them. Lastly, due to the masses of all terrestrial objects in the Quad being so similar, Qresh is not the true center of the Quad. rather, it too orbits the Quad’s true center of gravity (hereby _c.g._ ) so that its path around its sun resembles a spiral. (Qresh’s orbit around the c.g. is neglected in Figure 5.)

 

_Figure 5: Orbits of moons around Qresh. Flare indicates center of gravity; Qresh’s orbit around the c.g. is not shown. Top: Offside configuration. Bottom: Butterfly configuration. Terrestrial objects are on scale relative to each other, but not relative to anything else. Orbit are proportioned relative to each other, but not to anything else. Specifically, Leith’s orbit in the bottom panel should go around Qresh rather than intersect with it._

 

 _Option 1: The Offside._ In the first potential configuration (panel A, top), Qresh’s and Westerly’s orbits are both circles centered around the c.g., whereas Leith’s and Arkyn’s orbits are ellipses and offset to one side - away from the sun, presumably, else they would be all too likely to fall into it. (Earth’s moon leans away from our sun as well.) Qresh and Westerly are in synch with one another, and complete their orbits around the c.g. in the same time. (Making Qresh that much slower than Westerly, as its orbits is that much shorter.) In the same time, Arkyn complete approximately half its circuit and Leith completes almost three. Parts of Westerly’s orbit get it as near to Qresh as Leith’s but, due to their different speeds, they are rarely (if ever) at a similar distance from Qresh. For the same reasons, any two of the moons (let alone all three of them) rarely (if ever) align on the same axis.

 _Option 2: The Butterfly._ In the second potential configuration (panel B, bottom), Leith’s and Westerly’s orbits are both ellipses and Arkyn’s is a circle. (Qresh’s orbit is complicated, and will be discussed at the end of this paragraph.) Leith’s and Westerly’s orbits point in opposite directions (180 degrees from each other, or near-so). Each of them moves the fastest when passing behind Qresh (“slingshot”), and the slowest when far from it. Westerly completes one orbit for each 5-10 of Leith’s. It always slingshots around Qresh at the same time as (and to the opposite side of) Leith. Arkyn’s orbit is centered around the Quad’s c.g.; it completes one orbit for each 87% of Westerly’s (so 4-9 of Leith’s). Qresh’s orbit is comprised of two circular motions. The smaller circle is synched with Leith; that is, Qresh completes a small circle in the same time Leith completes one orbit around Qresh. The bigger circles is centered around the c.g., and synched with Westerly. The direction of Qresh’s motion around the c.g. is, at any point, the same as Leith’s. Possible alignments of the moons are discussed in the next paragraph.

 _Tidal forces._ Evidently, Qresh has nothing like Earth’s fairly simple diurnal or semi-diurnal tides. Rather, the rise and ebb of Qresh’s tide are the product of the combined movement of all three moons. Recall that in addition to the gravitational pull of each moon on its own, particularly massive tides called “spring tides” may occur when a moon is on the same axis with another relevant body. The magnitude of the “spring” effect depends on the masses and distances of all objects involved: the effect of mass is linear (twice the mass, twice the force) but the effect of distance is inverted to the third power (twice the distance, one-eighth the force). In the “Offside” orbital configuration the moons align rarely (if ever), so a total of six potential spring tides occur regularly. They are, in descending order of majority:

  * Major Leithian tide:  Leith is in-line with Qresh and the sun, at its nearest point to both (between them)
  * Minor Leithian tide: Leith is in-line with Qresh and the sun, at its farthest point from both (Qresh is in the middle)
  * Major Westerlyn tide: Westerly is aligned with the local sun, between it and Qresh
  * Minor Westerlyn tide: Westerly is aligned with the local sun, Qresh is between them
  * Major Arkynian tide: Arkyn is in-line with Qresh and the sun, at its nearest point to both (between them)
  * Minor Arkynian tide: Arkyn is in-line with Qresh and the sun, at its farthest point from both (Qresh is in the middle)



In the “Butterfly” orbital configuration, unlike the “Offside” one, the moons can and do align with one another. However, the axis on which they align is perpendicular to the imaginary line between Qresh and the sun. Thus, the “Butterfly” orbital configuration has a stupendous number of different spring tides. These are depicted in Figure 6 below.

 

_Figure 6: potential single-axis alignments of Qresh’s moons in the “Butterfly” orbital configuration. Panel A: potential alignments for 2 out of the 3 moons. Panel B: potential alignments involving all 3 moons. The sizes of the moons are depicted on scale to each other but not to other elements; the same to the r of their orbits. Arkyn - grey; Westerly - red; Leith - green; Qresh is not shown._

 

 _Seismic tides._ Lastly, recall that Qresh’s composition is different than Earth’s: Qresh is of a very low density and only barely solid. Though this low density means that it’s unlikely to have a molten metal core similar to Earth’s, and so unlikely to be subject to the same pressures driving Earth’s tectonic movement, it’s entirely possible that Qresh’s nominally solid parts are also affected by tidal forces, albeit to a more limited degree than its oceans. In the “Butterfly” alignment in particular, Qresh’s continents may shift constantly and unpredictably.

 _Climate._ Qresh and its moons are all at effectively the same distance from the local sun. It’s almost certain all their orbits are in the same plane, as any tilt would destabilize the system and make them all too likely to collide or else fly out of the system. Therefore, any climatic differences between these four terrestrial objects would be the result of other factors, such as their width, atmospheric content and topography.

 _Diurnal periods._ Qresh and Leith, being the prefered sites for human habitation, most likely have a diurnal period resulting from rotating on their own axes. This period is, in all likelihood, of appropriate length to support human sanity - so about 25 hours, give or take 5. Leith would also experience regular shading from Qresh. These shading events are likely to be quite short, due to Leith’s rapid orbit around Qresh; this is supported by Leith having regular enough light/dark conditions to support large-scale agriculture. Westerly is shown in canon to experience both light and dark conditions, but nothing is known about the regularity of these light and dark periods or whether they’re created by self-rotation or else shading by Qresh. Similarly, nothing is known about light and dark conditions on Arkyn.

 _It can always get worse._ There’s two other considerations that stood out to us, as we composed this essay. One is that we don’t actually know whether Qresh’s oceans are saltwater or freshwater. If the former, then flooding events will have catastrophic effects on the ecosystem, as large amounts of saltwater will harm plants and animals, and contaminate soil and groundwater - or else the Qreshi ecosystem may be adapted to this process, with organisms capable of flourishing (or at the very least surviving) under both conditions. The other consideration which occurred to us is that orbits in the Quad may not be as stable as they seem, and one or more of them may be deteriorating at such a rate that it will take millions of years for a collision to occur. (This is a normal scale for astrophysical processes.) Such a process will not be visible to Qreshi settlers, but it will nevertheless cause tidal patterns to shift is such a way that previously-habitable areas will become impossible to live in over the centuries.

##### Suggested Resources

  * [My Solar System](https://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html) simulator
  * [The Extrasolar Planets Encyclopedia](http://exoplanet.eu/catalog/)



 

### And a time for every question

 _Killjoys_ canon vacillates between a great attention to detail and continuity on some issues, and handwaving others. The astrophysics of the Quad and related matters (such as climatology) seem to fall into the category of “Both”. In a show so meticulously planned, the specificity of N’oa’s statement on the length of hokk season on Leith makes the statement stand out and calls attention to it. On the other hand, the show avoids making any committed, explicit statement (whether visually or in dialogue) on the relative placement and size of Qresh’s moons. This is a duality fannish creators may be familiar with: enough detail to make your fictional world come alive (part of which is consistency) but not so much detail as to bog the creator and the audience down.

In this work, we attempted to pay tribute to canon and provide an additional resource to other fannish creators while bearing in mind the same balance: to enrich, but not over-commit. This is why we provided (what we hope are) thorough explanations as well as recommendations for additional, more in-depth resources: so that those fellow fans who wish to form their own theories but lack the initial familiarity with the science side of it may have a better starting point. Where we suggest interpretations for existing canon, those are just that: interpretation and suggestions, a starting point for a discussion rather than the bottom line of one.

There exist oh-so-many more fascinating questions in this domain that we left unexplored. The last two paragraphs of the previous section touch on two: the nature of Qresh’s oceans and diurnal cycles of all terrestrial objects in the Quad. To this list one may also add the number and division of seasons on Leith, its source of water (given no large bodies of water are visible from space), climate on Westerly (and how it’s shaped by the extensive strip-mining), the mystery green liquid from Arkyn and, of course, a thorough discussion of Qresh’s tides. We let those questions lie, for now,  due to the degree of supposition involved in approaching them; but it is our hope that this work would be helpful to our fellow fans, when exploring those questions and others pertaining to the astrophysics of the Quad.

 

**Author's Note:**

> If you would like to use any of the figures, please (a) link back here and (b) provide an in-text reference, e.g. “Image from a meta by grimview and Hagar, available on the AO3”. Thank you!

**Works inspired by this one:**

  * [To every crop there is a season, and a time for every moon: Tabular Data](https://archiveofourown.org/works/5283896) by [Grimview](https://archiveofourown.org/users/Grimview/pseuds/Grimview), [Hagar](https://archiveofourown.org/users/Hagar/pseuds/Hagar)




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